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Boundary Value Problems 2011, 2011:51
doi:10.1186/1687-2770-2011-51

Published: 30 November 2011

Abstract

This paper is concerned with the existence of multiple unbounded solutions for a Sturm-Liouville
boundary value problem on the half-line. By assuming the existence of two pairs of
unbounded upper and lower solutions, the existence of at least three solutions is
obtained using the degree theories. Nagumo condition plays an important role in the
nonlinear term involved in the first-order derivative. It is an interesting point
that the method of unbounded upper and lower solutions is extended to obtain conditions
for the existence of multiple solutions.